Jimmy notices $7$ oranges weigh the same as $5$ apples.  If Jimmy has $28$ oranges, how many apples would Jimmy need to equal the weight of his $28$ oranges?
Answer: Since the weight of $7$ oranges is equal to the weight of $5$ apples, Jimmy needs only $5$ apples for every $7$ oranges in order for their weight to be equal.  So Jimmy needs $\frac{5}{7} \times 28=\boxed{20}$ apples.

Note: Read the problem carefully! It does not say that the ratio of the number of oranges to apples is 7:5. It says the ratio of the weight of oranges to apples is 7:5. This is a huge difference!